[3] | 1 | MODULE dynzdf_imp |
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| 2 | !!============================================================================== |
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| 3 | !! *** MODULE dynzdf_imp *** |
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| 4 | !! Ocean dynamics: vertical component(s) of the momentum mixing trend |
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| 5 | !!============================================================================== |
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[503] | 6 | !! History : ! 90-10 (B. Blanke) Original code |
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| 7 | !! ! 97-05 (G. Madec) vertical component of isopycnal |
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| 8 | !! 8.5 ! 02-08 (G. Madec) F90: Free form and module |
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| 9 | !!---------------------------------------------------------------------- |
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[3] | 10 | |
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| 11 | !!---------------------------------------------------------------------- |
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| 12 | !! dyn_zdf_imp : update the momentum trend with the vertical diffu- |
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| 13 | !! sion using a implicit time-stepping. |
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| 14 | !!---------------------------------------------------------------------- |
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[247] | 15 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[888] | 16 | !! $Id$ |
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[503] | 17 | !! Software governed by the CeCILL licence (modipsl/doc/NEMO_CeCILL.txt) |
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[3] | 18 | !!---------------------------------------------------------------------- |
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| 19 | !! * Modules used |
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| 20 | USE oce ! ocean dynamics and tracers |
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| 21 | USE dom_oce ! ocean space and time domain |
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[888] | 22 | USE sbc_oce ! surface boundary condition: ocean |
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| 23 | USE zdf_oce ! ocean vertical physics |
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[719] | 24 | USE phycst ! physical constants |
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[3] | 25 | USE in_out_manager ! I/O manager |
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| 26 | |
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| 27 | IMPLICIT NONE |
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| 28 | PRIVATE |
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| 29 | |
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| 30 | !! * Routine accessibility |
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| 31 | PUBLIC dyn_zdf_imp ! called by step.F90 |
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| 32 | |
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| 33 | !! * Substitutions |
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| 34 | # include "domzgr_substitute.h90" |
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| 35 | # include "vectopt_loop_substitute.h90" |
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| 36 | !!---------------------------------------------------------------------- |
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[247] | 37 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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[888] | 38 | !! $Id$ |
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[247] | 39 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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[3] | 40 | !!---------------------------------------------------------------------- |
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| 41 | |
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| 42 | CONTAINS |
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| 43 | |
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| 44 | |
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[503] | 45 | SUBROUTINE dyn_zdf_imp( kt, p2dt ) |
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[3] | 46 | !!---------------------------------------------------------------------- |
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| 47 | !! *** ROUTINE dyn_zdf_imp *** |
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| 48 | !! |
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| 49 | !! ** Purpose : Compute the trend due to the vert. momentum diffusion |
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| 50 | !! and the surface forcing, and add it to the general trend of |
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| 51 | !! the momentum equations. |
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| 52 | !! |
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| 53 | !! ** Method : The vertical momentum mixing trend is given by : |
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| 54 | !! dz( avmu dz(u) ) = 1/e3u dk+1( avmu/e3uw dk(ua) ) |
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| 55 | !! backward time stepping |
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| 56 | !! Surface boundary conditions: wind stress input |
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| 57 | !! Bottom boundary conditions : bottom stress (cf zdfbfr.F) |
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| 58 | !! Add this trend to the general trend ua : |
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| 59 | !! ua = ua + dz( avmu dz(u) ) |
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| 60 | !! |
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| 61 | !! ** Action : - Update (ua,va) arrays with the after vertical diffusive |
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| 62 | !! mixing trend. |
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| 63 | !!--------------------------------------------------------------------- |
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| 64 | !! * Modules used |
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[503] | 65 | USE oce, ONLY : zwd => ta, & ! use ta as workspace |
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| 66 | zws => sa ! use sa as workspace |
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[3] | 67 | |
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| 68 | !! * Arguments |
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[503] | 69 | INTEGER , INTENT( in ) :: kt ! ocean time-step index |
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| 70 | REAL(wp), INTENT( in ) :: p2dt ! vertical profile of tracer time-step |
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[3] | 71 | |
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| 72 | !! * Local declarations |
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[503] | 73 | INTEGER :: ji, jj, jk ! dummy loop indices |
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| 74 | REAL(wp) :: zrau0r, z2dtf, zcoef, zzws, zrhs ! temporary scalars |
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[1662] | 75 | REAL(wp) :: zzwi ! temporary scalars |
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[503] | 76 | REAL(wp), DIMENSION(jpi,jpj,jpk) :: zwi ! temporary workspace arrays |
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[3] | 77 | !!---------------------------------------------------------------------- |
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| 78 | |
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| 79 | IF( kt == nit000 ) THEN |
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| 80 | IF(lwp) WRITE(numout,*) |
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| 81 | IF(lwp) WRITE(numout,*) 'dyn_zdf_imp : vertical momentum diffusion implicit operator' |
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| 82 | IF(lwp) WRITE(numout,*) '~~~~~~~~~~~ ' |
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| 83 | ENDIF |
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| 84 | |
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| 85 | ! 0. Local constant initialization |
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| 86 | ! -------------------------------- |
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| 87 | zrau0r = 1. / rau0 ! inverse of the reference density |
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[455] | 88 | |
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[3] | 89 | ! 1. Vertical diffusion on u |
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| 90 | ! --------------------------- |
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| 91 | ! Matrix and second member construction |
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[1662] | 92 | ! bottom boundary condition: both zwi and zws must be masked as avmu can take |
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[3] | 93 | ! non zero value at the ocean bottom depending on the bottom friction |
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[1662] | 94 | ! used but the bottom velocities have already been updated with the bottom |
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| 95 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 96 | ! is no need to include these in the implicit calculation. |
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[3] | 97 | DO jk = 1, jpkm1 |
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| 98 | DO jj = 2, jpjm1 |
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| 99 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 100 | zcoef = - p2dt / fse3u(ji,jj,jk) |
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[1662] | 101 | zzwi = zcoef * avmu(ji,jj,jk ) / fse3uw(ji,jj,jk ) |
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| 102 | zwi(ji,jj,jk) = zzwi * umask(ji,jj,jk) |
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[3] | 103 | zzws = zcoef * avmu(ji,jj,jk+1) / fse3uw(ji,jj,jk+1) |
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| 104 | zws(ji,jj,jk) = zzws * umask(ji,jj,jk+1) |
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| 105 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
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| 106 | END DO |
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| 107 | END DO |
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| 108 | END DO |
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| 109 | |
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| 110 | ! Surface boudary conditions |
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| 111 | DO jj = 2, jpjm1 |
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| 112 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 113 | zwi(ji,jj,1) = 0. |
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| 114 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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| 115 | END DO |
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| 116 | END DO |
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| 117 | |
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| 118 | ! Matrix inversion starting from the first level |
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| 119 | !----------------------------------------------------------------------- |
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| 120 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 121 | ! |
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| 122 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 123 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 124 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 125 | ! ( ... )( ... ) ( ... ) |
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| 126 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 127 | ! |
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| 128 | ! m is decomposed in the product of an upper and a lower triangular matrix |
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| 129 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 130 | ! The solution (the after velocity) is in ua |
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| 131 | !----------------------------------------------------------------------- |
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| 132 | |
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| 133 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 134 | DO jk = 2, jpkm1 |
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| 135 | DO jj = 2, jpjm1 |
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| 136 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 137 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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| 138 | END DO |
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| 139 | END DO |
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| 140 | END DO |
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| 141 | |
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| 142 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 143 | DO jj = 2, jpjm1 |
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| 144 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 145 | !!! change les resultats (derniers digit, pas significativement + rapide 1* de moins) |
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| 146 | !!! ua(ji,jj,1) = ub(ji,jj,1) & |
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[888] | 147 | !!! + p2dt * ( ua(ji,jj,1) + utau(ji,jj) / ( fse3u(ji,jj,1)*rau0 ) ) |
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[503] | 148 | z2dtf = p2dt / ( fse3u(ji,jj,1)*rau0 ) |
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[3] | 149 | ua(ji,jj,1) = ub(ji,jj,1) & |
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[888] | 150 | + p2dt * ua(ji,jj,1) + z2dtf * utau(ji,jj) |
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[3] | 151 | END DO |
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| 152 | END DO |
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| 153 | DO jk = 2, jpkm1 |
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| 154 | DO jj = 2, jpjm1 |
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| 155 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 156 | zrhs = ub(ji,jj,jk) + p2dt * ua(ji,jj,jk) ! zrhs=right hand side |
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[3] | 157 | ua(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * ua(ji,jj,jk-1) |
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| 158 | END DO |
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| 159 | END DO |
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| 160 | END DO |
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| 161 | |
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| 162 | ! thrid recurrence : SOLk = ( Lk - Uk * Ek+1 ) / Dk |
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| 163 | DO jj = 2, jpjm1 |
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| 164 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 165 | ua(ji,jj,jpkm1) = ua(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 166 | END DO |
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| 167 | END DO |
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| 168 | DO jk = jpk-2, 1, -1 |
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| 169 | DO jj = 2, jpjm1 |
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| 170 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 171 | ua(ji,jj,jk) =( ua(ji,jj,jk) - zws(ji,jj,jk) * ua(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 172 | END DO |
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| 173 | END DO |
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| 174 | END DO |
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| 175 | |
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| 176 | ! Normalization to obtain the general momentum trend ua |
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| 177 | DO jk = 1, jpkm1 |
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| 178 | DO jj = 2, jpjm1 |
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| 179 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 180 | ua(ji,jj,jk) = ( ua(ji,jj,jk) - ub(ji,jj,jk) ) / p2dt |
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[3] | 181 | END DO |
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| 182 | END DO |
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| 183 | END DO |
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| 184 | |
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| 185 | |
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| 186 | ! 2. Vertical diffusion on v |
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| 187 | ! --------------------------- |
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| 188 | ! Matrix and second member construction |
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[1662] | 189 | ! bottom boundary condition: both zwi and zws must be masked as avmv can take |
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[3] | 190 | ! non zero value at the ocean bottom depending on the bottom friction |
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[1662] | 191 | ! used but the bottom velocities have already been updated with the bottom |
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| 192 | ! friction velocity in dyn_bfr using values from the previous timestep. There |
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| 193 | ! is no need to include these in the implicit calculation. |
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[3] | 194 | DO jk = 1, jpkm1 |
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| 195 | DO jj = 2, jpjm1 |
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| 196 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 197 | zcoef = -p2dt / fse3v(ji,jj,jk) |
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[1662] | 198 | zzwi = zcoef * avmv(ji,jj,jk ) / fse3vw(ji,jj,jk ) |
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| 199 | zwi(ji,jj,jk) = zzwi * vmask(ji,jj,jk) |
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[3] | 200 | zzws = zcoef * avmv(ji,jj,jk+1) / fse3vw(ji,jj,jk+1) |
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| 201 | zws(ji,jj,jk) = zzws * vmask(ji,jj,jk+1) |
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| 202 | zwd(ji,jj,jk) = 1. - zwi(ji,jj,jk) - zzws |
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| 203 | END DO |
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| 204 | END DO |
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| 205 | END DO |
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| 206 | |
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| 207 | ! Surface boudary conditions |
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| 208 | DO jj = 2, jpjm1 |
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| 209 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 210 | zwi(ji,jj,1) = 0.e0 |
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| 211 | zwd(ji,jj,1) = 1. - zws(ji,jj,1) |
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| 212 | END DO |
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| 213 | END DO |
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| 214 | |
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| 215 | ! Matrix inversion |
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| 216 | !----------------------------------------------------------------------- |
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| 217 | ! solve m.x = y where m is a tri diagonal matrix ( jpk*jpk ) |
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| 218 | ! |
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| 219 | ! ( zwd1 zws1 0 0 0 )( zwx1 ) ( zwy1 ) |
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| 220 | ! ( zwi2 zwd2 zws2 0 0 )( zwx2 ) ( zwy2 ) |
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| 221 | ! ( 0 zwi3 zwd3 zws3 0 )( zwx3 )=( zwy3 ) |
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| 222 | ! ( ... )( ... ) ( ... ) |
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| 223 | ! ( 0 0 0 zwik zwdk )( zwxk ) ( zwyk ) |
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| 224 | ! |
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| 225 | ! m is decomposed in the product of an upper and lower triangular |
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| 226 | ! matrix |
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| 227 | ! The 3 diagonal terms are in 2d arrays: zwd, zws, zwi |
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| 228 | ! The solution (after velocity) is in 2d array va |
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| 229 | !----------------------------------------------------------------------- |
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| 230 | |
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| 231 | ! First recurrence : Dk = Dk - Lk * Uk-1 / Dk-1 (increasing k) |
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| 232 | DO jk = 2, jpkm1 |
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| 233 | DO jj = 2, jpjm1 |
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| 234 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 235 | zwd(ji,jj,jk) = zwd(ji,jj,jk) - zwi(ji,jj,jk) * zws(ji,jj,jk-1) / zwd(ji,jj,jk-1) |
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| 236 | END DO |
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| 237 | END DO |
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| 238 | END DO |
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| 239 | |
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| 240 | ! second recurrence: SOLk = RHSk - Lk / Dk-1 Lk-1 |
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| 241 | DO jj = 2, jpjm1 |
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| 242 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 243 | !!! change les resultats (derniers digit, pas significativement + rapide 1* de moins) |
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| 244 | !!! va(ji,jj,1) = vb(ji,jj,1) & |
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[888] | 245 | !!! + p2dt * ( va(ji,jj,1) + vtau(ji,jj) / ( fse3v(ji,jj,1)*rau0 ) ) |
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[503] | 246 | z2dtf = p2dt / ( fse3v(ji,jj,1)*rau0 ) |
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[3] | 247 | va(ji,jj,1) = vb(ji,jj,1) & |
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[888] | 248 | + p2dt * va(ji,jj,1) + z2dtf * vtau(ji,jj) |
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[3] | 249 | END DO |
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| 250 | END DO |
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| 251 | DO jk = 2, jpkm1 |
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| 252 | DO jj = 2, jpjm1 |
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| 253 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 254 | zrhs = vb(ji,jj,jk) + p2dt * va(ji,jj,jk) ! zrhs=right hand side |
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[3] | 255 | va(ji,jj,jk) = zrhs - zwi(ji,jj,jk) / zwd(ji,jj,jk-1) * va(ji,jj,jk-1) |
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| 256 | END DO |
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| 257 | END DO |
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| 258 | END DO |
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| 259 | |
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| 260 | ! thrid recurrence : SOLk = ( Lk - Uk * SOLk+1 ) / Dk |
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| 261 | DO jj = 2, jpjm1 |
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| 262 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 263 | va(ji,jj,jpkm1) = va(ji,jj,jpkm1) / zwd(ji,jj,jpkm1) |
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| 264 | END DO |
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| 265 | END DO |
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| 266 | DO jk = jpk-2, 1, -1 |
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| 267 | DO jj = 2, jpjm1 |
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| 268 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 269 | va(ji,jj,jk) =( va(ji,jj,jk) - zws(ji,jj,jk) * va(ji,jj,jk+1) ) / zwd(ji,jj,jk) |
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| 270 | END DO |
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| 271 | END DO |
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| 272 | END DO |
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| 273 | |
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| 274 | ! Normalization to obtain the general momentum trend va |
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| 275 | DO jk = 1, jpkm1 |
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| 276 | DO jj = 2, jpjm1 |
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| 277 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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[503] | 278 | va(ji,jj,jk) = ( va(ji,jj,jk) - vb(ji,jj,jk) ) / p2dt |
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[3] | 279 | END DO |
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| 280 | END DO |
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| 281 | END DO |
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| 282 | |
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| 283 | END SUBROUTINE dyn_zdf_imp |
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| 284 | |
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| 285 | !!============================================================================== |
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| 286 | END MODULE dynzdf_imp |
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